Origi, 22, joined Liverpool from French side Lille for £10million in 2014.
However, he has failed to hit the heights at Anfield and has fallen down the pecking order under Jurgen Klopp.
The Belgium international is yet to start to a game for the Reds this season, with his only Premier League outing coming against Watford.
Klopp has refused to rule out the prospect of Origi leaving Liverpool if more signings are made before the transfer window closes on August 31.
Tottenham have apparently expressed an interest in the striker as Mauricio Pochettino looks to bolster his attacking ranks.

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Spurs only have Vincent Janssen to provide cover for Harry Kane, but with the former being allowed to leave the club they would need to sign a replacement.
And Origi’s father Mike reckons a move to Tottenham could be a possibility as his soon needs regular game time.
But he also outlined he has several other options from France and Germany to consider too.
“Divock has to leave Liverpool to get more playing time,” he told Belgium outlet DH.be.
“Tottenham is a possibility, but there is also interest from France and Germany.”
Origi has scored 21 goals in 76 appearances for Liverpool since joining after the 2014 World Cup.
He is contracted to the club until the summer of 2019.